I've had this tenor mouthpiece for a couple of years. I don't use it
because I can't stand the burnt rubber smell of it.
On the odd occasion that I have blown it I can get quite a nice sound
out of it but with a lot of effort. I've just had a look at the lay.
It could explain a bit. The 2cm back from the tip is very nearly flat
- hardly curved at all. Then there is quite an abrupt kink which takes
the lay to a much shallower angle to meet the table. I can't help
feeling this is not a good shape for the reed to try and bend round. 
Has anyone seen one of these before? Was it the same, or have I just
got a duffer?
I'm afraid I don't have the gear to do accurate measurements on it.

I think your instict is correct.  A kink in the facing would add resistance
to the blowing of the piece.  There could also be very small air leaks
since the reed can not conform to a sharp kink.  I do not think this is a
feature of the JDX8.

Clarinet facings often have 2 kinks in them, but they are blended in.  More
like 3 flat sections with curved transistions between them.  I do not fully
understand clarinet pieces, but I believe that this facing shape gives them
a nice resistance where the clarinet player wants it.

You can try to blend in the kinks on your JDX8. Use some 600 grit sandpaper
on a countertop and lighty drag the kink over it.  By inspecting the piece
after each drag, you can see if you are holding it at the proper angle to
sand at the kink.

Someone on SOTW posted that they are using a coating a wax (Canoba?) to
seal in the rubber smell.

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Thanks Keith,
I tried your suggestion. It still stinks but it's a lot easier to blow.
I'll try the wax treatment next.
Nick